Finite Group Databasebeta

← C151×#18974 #50323899

Subgroups — C151×#18974 #50323899

Order 38656.

930 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3546×C151C211yesmaximal, characteristic
2#3254×C151C211yesmaximal, characteristic, complemented
3#3248×C151C211yesmaximal, characteristic, complemented
4#3228×C151C211yesmaximal, characteristic, complemented
5#1654×C151C211yesmaximal, characteristic, complemented
6#1652×C151C211yesmaximal, characteristic, complemented
7#1650×C151C211yesmaximal, characteristic, complemented
8#1647×C151C211yesmaximal, characteristic, complemented
9#1642×C151C211yesmaximal, characteristic, complemented
10#1641×C151C211yesmaximal, characteristic, complemented
11#1639×C151C211yesmaximal, characteristic, complemented
12#1639×C151C211yesmaximal, characteristic, complemented
13#1547×C151C211yesmaximal, characteristic, complemented
14#1495×C151C211yesmaximal, characteristic, complemented
15#1480×C151C211yesmaximal, characteristic, complemented
16#560×C151—22no—
17#556×C151C2211yescharacteristic
18#553×C151—21no—
19#550×C151—21no—
20#550×C151C2211yescharacteristic
21#547×C151C2211yescharacteristic
22#546×C151—21no—
23#546×C151—21no—
24D42×C151C2211yescharacteristic
25#542×C151—21no—
26#538×C151—22no—
27#537×C151—21no—
28#535×C151—21no—
29#535×C151—21no—
30#533×C151C2211yescharacteristic, complemented
31#532×C151C2211yescharacteristic
32#532×C151C2211yescharacteristic
33#529×C151C2211yescharacteristic
34#500×C151C2211yescharacteristic, complemented
35#498×C151C2211yescharacteristic, complemented
36#486×C151C2211yescharacteristic
37#486×C151C2211yescharacteristic
38#482×C151—22no—
39#479×C151—21no—
40#478×C151—22no—
41#477×C151—21no—
42#475×C151C2211yescharacteristic, complemented
43#474×C151C2211yescharacteristic
44#474×C151C2211yescharacteristic
45#474×C151C2211yescharacteristic, complemented
46#468×C151—21no—
47#468×C151—21no—
48#467×C151—21no—
49#465×C151—21no—
50#464×C151—21no—
51#462×C151C2211yescharacteristic, complemented
52#461×C151C2211yescharacteristic
53#461×C151C2211yescharacteristic
54#461×C151C2211yescharacteristic, complemented
55#460×C151—21no—
56#431×C151C2211yescharacteristic, complemented
57#423×C151C2211yescharacteristic, complemented
58C2×C4⋊C8×C151C2211yescharacteristic, complemented
59#332×C151C2211yescharacteristic, complemented
60#332×C151C2211yescharacteristic, complemented
61#331×C151C2211yescharacteristic
62#331×C151C2211yescharacteristic
63Q8⋊C8×C151C2211yescharacteristic, complemented
64Q8⋊C8×C151C2211yescharacteristic, complemented
65D4⋊C8×C151C2211yescharacteristic
66D4⋊C8×C151C2211yescharacteristic
67D4⋊C8×C151C2211yescharacteristic
68D4⋊C8×C151C2211yescharacteristic
69D4⋊C8×C151C2211yescharacteristic, complemented
70D4⋊C8×C151C2211yescharacteristic, complemented
71C2×#41×C151—21no—
72C2×#41×C151—21no—
73C2×#41×C151—21no—
74C2×#41×C151—21no—
75C22×D4×C151—21no—
76C22×D4×C151—21no—
77C2×Q16×C151—21no—
78C2×SD16×C151—21no—
79C2×SD16×C151—21no—
80C2×SD16×C151—21no—
81C2×M16×C151—21no—
82C22×C8×C151—21no—
83C4⋊Q8×C151D411yescharacteristic
84C4⋊Q8×C151C2311yescharacteristic
85C4⋊Q8×C151C2311yescharacteristic
86C4⋊Q8×C151C2311yescharacteristic
87#127×C151—22no—
88#127×C151—21no—
89#127×C151D411yescharacteristic
90#127×C151C2311yescharacteristic
91#126×C151—22no—
92#126×C151—22no—
93#126×C151—21no—
94#125×C151—21no—
95#125×C151D411yescharacteristic
96#124×C151—22no—
97#124×C151—21no—
98#124×C151—21no—
99#124×C151—21no—
100#124×C151D411yescharacteristic
101#123×C151—22no—
102#123×C151—22no—
103#123×C151—21no—
104#123×C151—22no—
105C22⋊Q8×C151—22no—
106C22⋊Q8×C151—21no—
107C22⋊Q8×C151—21no—
108C22⋊Q8×C151—21no—
109C22⋊Q8×C151—21no—
110C22⋊Q8×C151D411yescharacteristic
111#121×C151—22no—
112#121×C151—22no—
113#121×C151—22no—
114#121×C151—22no—
115#121×C151—22no—
116#121×C151—21no—
117#121×C151—22no—
118#121×C151—21no—
119#121×C151—21no—
120#121×C151—21no—
121#121×C151—21no—
122#121×C151—21no—
123#121×C151D411yescharacteristic
124#121×C151D411yescharacteristic
125#121×C151D411yescharacteristic
126#121×C151D412yes—
127#120×C151—22no—
128#120×C151—22no—
129#120×C151—22no—
130#120×C151—22no—
131C4×Q8×C151—21no—
132C4×Q8×C151—21no—
133C4×Q8×C151—21no—
134C4×Q8×C151C2311yescharacteristic
135C4×D4×C151—22no—
136C4×D4×C151—21no—
137C4×D4×C151—21no—
138C4×D4×C151—21no—
139C4×D4×C151—21no—
140C4×D4×C151D412yes—
141C4×D4×C151C2311yescharacteristic
142C4×D4×C151C2311yescharacteristic
143C4×D4×C151C2311yescharacteristic
144#117×C151—21no—
145#117×C151—21no—
146#117×C151—21no—
147C2×C4⋊C4×C151—21no—
148C2×C22⋊C4×C151—22no—
149C2×C42×C151C2311yescharacteristic
150#107×C151—21no—
151#107×C151—21no—
152#107×C151—21no—
153#107×C151—22no—
154#106×C151—21no—
155#106×C151—22no—
156C4⋊C8×C151—21no—
157C4⋊C8×C151—21no—
158C4⋊C8×C151—21no—
159C4⋊C8×C151C2311yescharacteristic
160C4⋊C8×C151C2311yescharacteristic
161C4⋊C8×C151C2311yescharacteristic
162C4⋊C8×C151C2311yescharacteristic
163#103×C151—21no—
164#103×C151—21no—
165#103×C151—21no—
166#103×C151—21no—
167#103×C151—21no—
168#102×C151—21no—
169#102×C151—21no—
170#102×C151—21no—
171#102×C151—22no—
172#102×C151—22no—
173C22⋊C8×C151—21no—
174C4×C8×C151C2311yescharacteristic
175C4×C8×C151C2311yescharacteristic
176C24×C151—22no—
177#41×C151—81no—
178#41×C151—81no—
179#41×C151—81no—
180#41×C151—81no—
181#41×C151—81no—
182#41×C151—81no—
183#41×C151—81no—
184#41×C151—81no—
185C2×Q8×C151—21no—
186C2×Q8×C151—21no—
187C2×Q8×C151—21no—
188C2×Q8×C151—21no—
189C2×Q8×C151C2×D411yescharacteristic
190C2×D4×C151—22no—
191C2×D4×C151—22no—
192C2×D4×C151—22no—
193C2×D4×C151—22no—
194C2×D4×C151—22no—
195C2×D4×C151—21no—
196C2×D4×C151—21no—
197C2×D4×C151—22no—
198C2×D4×C151—21no—
199C2×D4×C151—21no—
200C2×D4×C151—21no—
201C2×D4×C151—21no—
202C2×D4×C151—21no—
203C2×D4×C151—81no—
204C2×D4×C151—81no—
205C2×D4×C151—81no—
206C2×D4×C151—81no—
207C2×D4×C151C2×D411yescharacteristic
208C2×D4×C151C2×D411yescharacteristic
209C2×D4×C151C2×D411yescharacteristic
210C2×D4×C151C2×D412yes—
211C22×C4×C151—22no—
212C22×C4×C151—22no—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—22no—
217C22×C4×C151C2×D411yescharacteristic
218C22×C4×C151C2×D411yescharacteristic
219C22×C4×C151C2×D411yescharacteristic
220Q16×C151—81no—
221SD16×C151—81no—
222SD16×C151—81no—
223SD16×C151—81no—
224M16×C151—81no—
225C2×C8×C151—21no—
226C2×C8×C151—21no—
227C2×C8×C151—21no—
228C2×C8×C151—21no—
229C2×C8×C151—21no—
230C2×C8×C151—21no—
231C2×C8×C151—81no—
232C4⋊C4×C151—22no—
233C4⋊C4×C151—22no—
234C4⋊C4×C151—21no—
235C4⋊C4×C151—21no—
236C4⋊C4×C151—21no—
237C4⋊C4×C151—21no—
238C4⋊C4×C151—21no—
239C4⋊C4×C151—21no—
240C4⋊C4×C151—21no—
241C4⋊C4×C151—21no—
242C4⋊C4×C151—21no—
243C4⋊C4×C151—21no—
244C4⋊C4×C151—41no—
245C4⋊C4×C151—41no—
246C4⋊C4×C151C2×D411yescharacteristic
247C4⋊C4×C151C2×D411yescharacteristic
248C4⋊C4×C151C2×D411yescharacteristic
249C4⋊C4×C151C2×D411yescharacteristic
250C4⋊C4×C151C2×D412yes—
251C22⋊C4×C151—22no—
252C22⋊C4×C151—22no—
253C22⋊C4×C151—22no—
254C22⋊C4×C151—22no—
255C22⋊C4×C151—22no—
256C22⋊C4×C151—21no—
257C22⋊C4×C151—21no—
258C22⋊C4×C151—21no—
259C22⋊C4×C151—21no—
260C22⋊C4×C151—21no—
261C22⋊C4×C151—21no—
262C22⋊C4×C151—22no—
263C22⋊C4×C151—22no—
264C22⋊C4×C151—21no—
265C22⋊C4×C151—21no—
266C22⋊C4×C151—21no—
267C22⋊C4×C151—41no—
268C42×C151—22no—
269C42×C151—21no—
270C42×C151—41no—
271C42×C151C2×D411yescharacteristic
272C42×C151C2×D411yescharacteristic
273C42×C151C2×D411yescharacteristic
274C42×C151C2411yescharacteristic
275C23×C151—21no—
276C23×C151—21no—
277C23×C151—22no—
278C23×C151—21no—
279C23×C151—82no—
280C23×C151—82no—
281C23×C151—82no—
282C23×C151#12011yescharacteristic
283Q8×C151—21no—
284Q8×C151—21no—
285Q8×C151—41no—
286Q8×C151—41no—
287Q8×C151—41no—
288Q8×C151—41no—
289Q8×C151—41no—
290Q8×C151—41no—
291Q8×C151—81no—
292D4×C151—21no—
293D4×C151—21no—
294D4×C151—21no—
295D4×C151—21no—
296D4×C151—21no—
297D4×C151—21no—
298D4×C151—42no—
299D4×C151—41no—
300D4×C151—41no—
301D4×C151—41no—
302D4×C151—41no—
303D4×C151—81no—
304D4×C151—81no—
305D4×C151—81no—
306D4×C151—81no—
307D4×C151—82no—
308D4×C151—81no—
309D4×C151—82no—
310D4×C151—82no—
311D4×C151—82no—
312D4×C151—82no—
313D4×C151—82no—
314C2×C4×C151—21no—
315C2×C4×C151—21no—
316C2×C4×C151—21no—
317C2×C4×C151—21no—
318C2×C4×C151—21no—
319C2×C4×C151—22no—
320C2×C4×C151—21no—
321C2×C4×C151—21no—
322C2×C4×C151—21no—
323C2×C4×C151—21no—
324C2×C4×C151—41no—
325C2×C4×C151—41no—
326C2×C4×C151—41no—
327C2×C4×C151—41no—
328C2×C4×C151—41no—
329C2×C4×C151—41no—
330C2×C4×C151—41no—
331C2×C4×C151—41no—
332C2×C4×C151—41no—
333C2×C4×C151—82no—
334C2×C4×C151—82no—
335C2×C4×C151—82no—
336C2×C4×C151#12011yescharacteristic
337C2×C4×C151#12011yescharacteristic
338C2×C4×C151#12011yescharacteristic
339C2×C4×C151C22×D411yescharacteristic
340C2×C4×C151C22×D411yescharacteristic
341C2×C4×C151C22×D411yescharacteristic
342C8×C151—41no—
343C8×C151—41no—
344C8×C151—41no—
345C8×C151—41no—
346C8×C151—41no—
347C8×C151—41no—
348C22×C151—21no—
349C22×C151—21no—
350C22×C151—21no—
351C22×C151—41no—
352C22×C151—41no—
353C22×C151—41no—
354C22×C151—41no—
355C22×C151—42no—
356C22×C151—42no—
357C22×C151—41no—
358C22×C151—41no—
359C22×C151—42no—
360C22×C151—41no—
361C22×C151—41no—
362C22×C151—41no—
363C22×C151—164no—
364C22×C151C2×#12011yescharacteristic
365C4×C151—21no—
366C4×C151—21no—
367C4×C151—21no—
368C4×C151—21no—
369C4×C151—41no—
370C4×C151—41no—
371C4×C151—41no—
372C4×C151—41no—
373C4×C151—42no—
374C4×C151—41no—
375C4×C151—81no—
376C4×C151—81no—
377C4×C151#57611yescharacteristic
378C4×C151#57611yescharacteristic
379C4×C151#57711yescharacteristic
380C4×C151#57711yescharacteristic
381C2×C151—41no—
382C2×C151—81no—
383C2×C151—82no—
384C2×C151—81no—
385C2×C151—81no—
386C2×C151#301211yescharacteristic
387C2×C151#301211yescharacteristic
388C2×C151#302211yescharacteristic
389#18974C15111yesmaximal, characteristic, direct product factor, Sylow
390C151#1897411yescharacteristic, direct product factor, Sylow
391#3546C2×C15111yescharacteristic
392#3254C2×C15111yescharacteristic, complemented
393#3248C2×C15111yescharacteristic, complemented
394#3228C2×C15111yescharacteristic, complemented
395#1654C2×C15111yescharacteristic, complemented
396#1652C2×C15111yescharacteristic, complemented
397#1650C2×C15111yescharacteristic, complemented
398#1647C2×C15111yescharacteristic, complemented
399#1642C2×C15111yescharacteristic, complemented
400#1641C2×C15111yescharacteristic, complemented
401#1639C2×C15111yescharacteristic, complemented
402#1639C2×C15111yescharacteristic, complemented
403#1547C2×C15111yescharacteristic, complemented
404#1495C2×C15111yescharacteristic, complemented
405#1480C2×C15111yescharacteristic, complemented
406#560—22no—
407#556C22×C15111yescharacteristic
408#553—21no—
409#550—21no—
410#550C22×C15111yescharacteristic
411#547C22×C15111yescharacteristic
412#546—21no—
413#546—21no—
414D42C22×C15111yescharacteristic
415#542—21no—
416#538—22no—
417#537—21no—
418#535—21no—
419#535—21no—
420#533C22×C15111yescharacteristic, complemented
421#532C22×C15111yescharacteristic
422#532C22×C15111yescharacteristic
423#529C22×C15111yescharacteristic
424#500C22×C15111yescharacteristic, complemented
425#498C22×C15111yescharacteristic, complemented
426#486C22×C15111yescharacteristic
427#486C22×C15111yescharacteristic
428#482—22no—
429#479—21no—
430#478—22no—
431#477—21no—
432#475C22×C15111yescharacteristic, complemented
433#474C22×C15111yescharacteristic
434#474C22×C15111yescharacteristic
435#474C22×C15111yescharacteristic, complemented
436#468—21no—
437#468—21no—
438#467—21no—
439#465—21no—
440#464—21no—
441#462C22×C15111yescharacteristic, complemented
442#461C22×C15111yescharacteristic
443#461C22×C15111yescharacteristic
444#461C22×C15111yescharacteristic, complemented
445#460—21no—
446#431C22×C15111yescharacteristic, complemented
447#423C22×C15111yescharacteristic, complemented
448C2×C4⋊C8C22×C15111yescharacteristic, complemented
449#332C22×C15111yescharacteristic, complemented
450#332C22×C15111yescharacteristic, complemented
451#331C22×C15111yescharacteristic
452#331C22×C15111yescharacteristic
453Q8⋊C8C22×C15111yescharacteristic, complemented
454Q8⋊C8C22×C15111yescharacteristic, complemented
455D4⋊C8C22×C15111yescharacteristic
456D4⋊C8C22×C15111yescharacteristic
457D4⋊C8C22×C15111yescharacteristic
458D4⋊C8C22×C15111yescharacteristic
459D4⋊C8C22×C15111yescharacteristic, complemented
460D4⋊C8C22×C15111yescharacteristic, complemented
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C22×D4—21no—
466C22×D4—21no—
467C2×Q16—21no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×M16—21no—
472C22×C8—21no—
473C4⋊Q8D4×C15111yescharacteristic
474C4⋊Q8C23×C15111yescharacteristic
475C4⋊Q8C23×C15111yescharacteristic
476C4⋊Q8C23×C15111yescharacteristic
477#127—22no—
478#127—21no—
479#127D4×C15111yescharacteristic
480#127C23×C15111yescharacteristic
481#126—22no—
482#126—22no—
483#126—21no—
484#125—21no—
485#125D4×C15111yescharacteristic
486#124—22no—
487#124—21no—
488#124—21no—
489#124—21no—
490#124D4×C15111yescharacteristic
491#123—22no—
492#123—22no—
493#123—21no—
494#123—22no—
495C22⋊Q8—22no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8D4×C15111yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—21no—
507#121—22no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121D4×C15111yescharacteristic
514#121D4×C15111yescharacteristic
515#121D4×C15111yescharacteristic
516#121D4×C15112yes—
517#120—22no—
518#120—22no—
519#120—22no—
520#120—22no—
521C4×Q8—21no—
522C4×Q8—21no—
523C4×Q8—21no—
524C4×Q8C23×C15111yescharacteristic
525C4×D4—22no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4D4×C15112yes—
531C4×D4C23×C15111yescharacteristic
532C4×D4C23×C15111yescharacteristic
533C4×D4C23×C15111yescharacteristic
534#117—21no—
535#117—21no—
536#117—21no—
537C2×C4⋊C4—21no—
538C2×C22⋊C4—22no—
539C2×C42C23×C15111yescharacteristic
540#107—21no—
541#107—21no—
542#107—21no—
543#107—22no—
544#106—21no—
545#106—22no—
546C4⋊C8—21no—
547C4⋊C8—21no—
548C4⋊C8—21no—
549C4⋊C8C23×C15111yescharacteristic
550C4⋊C8C23×C15111yescharacteristic
551C4⋊C8C23×C15111yescharacteristic
552C4⋊C8C23×C15111yescharacteristic
553#103—21no—
554#103—21no—
555#103—21no—
556#103—21no—
557#103—21no—
558#102—21no—
559#102—21no—
560#102—21no—
561#102—22no—
562#102—22no—
563C22⋊C8—21no—
564C4×C8C23×C15111yescharacteristic
565C4×C8C23×C15111yescharacteristic
566C24—22no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573#41—81no—
574#41—81no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8C2×D4×C15111yescharacteristic
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4C2×D4×C15111yescharacteristic
598C2×D4C2×D4×C15111yescharacteristic
599C2×D4C2×D4×C15111yescharacteristic
600C2×D4C2×D4×C15112yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4C2×D4×C15111yescharacteristic
608C22×C4C2×D4×C15111yescharacteristic
609C22×C4C2×D4×C15111yescharacteristic
610Q16—81no—
611SD16—81no—
612SD16—81no—
613SD16—81no—
614M16—81no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—81no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4C2×D4×C15111yescharacteristic
637C4⋊C4C2×D4×C15111yescharacteristic
638C4⋊C4C2×D4×C15111yescharacteristic
639C4⋊C4C2×D4×C15111yescharacteristic
640C4⋊C4C2×D4×C15112yes—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—41no—
658C42—22no—
659C42—21no—
660C42—41no—
661C42C2×D4×C15111yescharacteristic
662C42C2×D4×C15111yescharacteristic
663C42C2×D4×C15111yescharacteristic
664C42C24×C15111yescharacteristic
665C23—21no—
666C23—21no—
667C23—22no—
668C23—21no—
669C23—82no—
670C23—82no—
671C23—82no—
672C23#120×C15111yescharacteristic
673Q8—21no—
674Q8—21no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—81no—
682D4—21no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—42no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697D4—82no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4#120×C15111yescharacteristic
727C2×C4#120×C15111yescharacteristic
728C2×C4#120×C15111yescharacteristic
729C2×C4C22×D4×C15111yescharacteristic
730C2×C4C22×D4×C15111yescharacteristic
731C2×C4C22×D4×C15111yescharacteristic
732C8—41no—
733C8—41no—
734C8—41no—
735C8—41no—
736C8—41no—
737C8—41no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—164no—
754C22C2×#120×C15111yescharacteristic
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—42no—
764C4—41no—
765C4—81no—
766C4—81no—
767C4#576×C15111yescharacteristic
768C4#576×C15111yescharacteristic
769C4#577×C15111yescharacteristic
770C4#577×C15111yescharacteristic
771C2—41no—
772C2—81no—
773C2—81no—
774C2—82no—
775C2—81no—
776C2#3012×C15111yescharacteristic
777C2#3012×C15111yescharacteristic
778C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3546×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #3254×C151C2semidirect
3. #3248×C151C2semidirect
4. #3228×C151C2semidirect
5. #1654×C151C2semidirect
6. #1652×C151C2semidirect
7. #1650×C151C2semidirect
8. #1647×C151C2semidirect
9. #1642×C151C2semidirect
10. #1641×C151C2semidirect
11. #1639×C151C2semidirect
12. #1639×C151C2semidirect
13. #1547×C151C2semidirect
14. #1495×C151C2semidirect
15. #1480×C151C2semidirect
30. #533×C151C22semidirect
34. #500×C151C22semidirect
35. #498×C151C22semidirect
42. #475×C151C22semidirect
45. #474×C151C22semidirect
51. #462×C151C22semidirect
54. #461×C151C22semidirect
56. #431×C151C22semidirect
57. #423×C151C22semidirect
58. C2×C4⋊C8×C151C22semidirect
59. #332×C151C22semidirect
60. #332×C151C22semidirect
63. Q8⋊C8×C151C22semidirect
64. Q8⋊C8×C151C22semidirect
69. D4⋊C8×C151C22semidirect
70. D4⋊C8×C151C22semidirect
389. #18974C151direct (N × H)
390. C151#18974direct (N × H)
392. #3254C2×C151semidirect
393. #3248C2×C151semidirect
394. #3228C2×C151semidirect
395. #1654C2×C151semidirect
396. #1652C2×C151semidirect
397. #1650C2×C151semidirect
398. #1647C2×C151semidirect
399. #1642C2×C151semidirect
400. #1641C2×C151semidirect
401. #1639C2×C151semidirect
402. #1639C2×C151semidirect
403. #1547C2×C151semidirect
404. #1495C2×C151semidirect
405. #1480C2×C151semidirect
420. #533C22×C151semidirect
424. #500C22×C151semidirect
425. #498C22×C151semidirect
432. #475C22×C151semidirect
435. #474C22×C151semidirect
441. #462C22×C151semidirect
444. #461C22×C151semidirect
446. #431C22×C151semidirect
447. #423C22×C151semidirect
448. C2×C4⋊C8C22×C151semidirect
449. #332C22×C151semidirect
450. #332C22×C151semidirect
453. Q8⋊C8C22×C151semidirect
454. Q8⋊C8C22×C151semidirect
459. D4⋊C8C22×C151semidirect
460. D4⋊C8C22×C151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#3546×C1512
#3254×C1512
#3248×C1512
#3228×C1512
#1654×C1512
#1652×C1512
#1650×C1512
#1647×C1512
#1642×C1512
#1641×C1512
#1639×C1512
#1547×C1512
#1495×C1512
#1480×C1512
#18974151